Research Papers

Numerical Study of Laminar Flow and Mass Transfer for In-Line Spacer-Filled Passages

[+] Author and Article Information
Steven B. Beale

Fellow ASME
National Research Council,
Montreal Road,
Ottawa, ON, K1A 0R6, Canada
e-mail: steven.beale@nrc-cnrc.gc.ca

Jon G. Pharoah

Department of Mechanical and Materials Engineering,
Queen’s University,
Kingston, ON, K7L 3N6, Canada
e-mail: pharoah@me.queensu.ca

Ashwani Kumar

National Research Council,
Montreal Road,
Ottawa, ON, K1A 0R6, Canada
e-mail: ashwani.kumar@nrc-cnrc.gc.ca

Manuscript received October 25, 2010; final manuscript received August 16, 2012; published online December 6, 2012. Assoc. Editor: Gerard F. Jones.

J. Heat Transfer 135(1), 011004 (Dec 06, 2012) (8 pages) Paper No: HT-10-1494; doi: 10.1115/1.4007651 History: Received October 25, 2010; Revised August 16, 2012

Performance calculations for laminar fluid flow and mass transfer are presented for a passage containing cylindrical spacers configured in an inline-square arrangement, typical of those employed in the process industries. Numerical calculations are performed for fully-developed flow, based on stream-wise periodic conditions for a unit cell and compared with those obtained for developing regime in a row of ten such units. The method is validated for an empty passage, i.e., a plane duct. Results are presented for the normalized mass transfer coefficient and driving force, as a function of mean flow Reynolds number, and also the wall mass flux, or blowing parameter. Both constant and variable wall velocities were considered, the latter being typical of those found in many practical membrane modules.

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Fig. 1

Schematic of spiral-wound membrane module showing details of Conwed spacer geometry

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Fig. 8

Friction and mass transfers factor, fully-developed periodic flow, constant vw

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Fig. 9

Mass fraction of retentate, yw, at surfaces 1 and 2, Re0 = 80, constant vw

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Fig. 10

Local values of Sh at surfaces 1 and 2, Re0 = 80, constant vw

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Fig. 3

Benchmark studies for a plane duct

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Fig. 4

Normalized spot values, periodic boundaries

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Fig. 5

Residual plot, periodic boundaries

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Fig. 6

Friction and mass transfer factors for multirow developing and fully-developed periodic flow. Re0 = 20 (upper) and Re0 = 60 (lower).

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Fig. 7

Flow visualization for Re0 = 80

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Fig. 11

Osmotic pressure as a function of retentate mass fraction for NaCl-brine, adapted from Pharoah [31]

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Fig. 2

Grid details (a) single unit and (b) 10 unit cells

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Fig. 12

Mass flux, m·″, of permeate at surfaces 1 and 2, Re0 = 80, vw = v0 + Ayw

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Fig. 13

High rate mass transfer factors, constant vw



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